During the C-section the nurse asked my wife if she would like to do skin to skin after the baby was born. Which of course anyone would say yes too. We just noticed it in the bill today.
The nurse let me hold the baby on my wife's neck/chest. Even borrowed my camera to take a few pictures for us.
Everyone involved in the process was great, and we had a positive experience. We just got a chuckle out of seeing that on the bill.

Most people probably wouldn't assume they'd be charged to hold their own child. It's the most natural thing to do once the baby is born.

But it's apparently not free.

In the comments for the dad's post on Reddit, a labor and delivery nurse expanded on why these parents were likely charged for holding their own newborn,

As a labor and delivery nurse, I can kind of explain this.
I didn't know that hospitals charged for it, but doing 'skin to skin' in the operating room requires an additional staff member to be present just to watch the baby.
We used to take all babies to the nursery once the NICU team made sure everything was okay.
'Skin to skin' in the OR is a relatively new thing and requires a second Labor and Delivery RN to come in to the OR and make sure the baby is safe.

While these parents seem to have a pretty good attitude about this, it's emblematic of how expensive healthcare in the US can be. This is especially true when it comes to childbirth.